Heat butter and olive oil in a large skillet over medium heat. Add sliced onions slowly and stir often. Cook them until soft, golden and slightly sweet. This process takes time but gives rich French onion flavor.

Add minced garlic to the onions and cook for one minute. Then add ground beef into the skillet. Break the meat into small pieces using a spoon. Cook until beef is browned and no pink remains.

Sprinkle flour over the beef mixture and stir well. Slowly pour in beef broth while mixing. Add Worcestershire sauce, soy sauce, sugar, salt, black pepper and thyme. Let it simmer until the sauce becomes slightly thick.

Lower the heat and let the mixture cook gently. Stir occasionally so nothing sticks to the pan. The sauce should become rich and slightly glossy. This step helps the flavors blend deeply together.

Cut hamburger buns in half and lightly toast them in a pan or oven. Toasting gives a crispy texture that holds the juicy filling better. This step also adds extra flavor and structure.

Spoon the beef and onion mixture onto the bottom half of each bun. Add a generous amount of shredded cheese on top. Place the top bun gently and press slightly before serving warm.